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Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the…
We establish the equivalence between the Multiscale Hybrid-Mixed (MHM) and the Multiscale Hybrid High-Order (MsHHO) methods for a variable diffusion problem with piecewise polynomial source term. Under the idealized assumption that the…
We introduce hierarchical mixtures of Gaussians (HMoGs), which unify dimensionality reduction and clustering into a single probabilistic model. HMoGs provide closed-form expressions for the model likelihood, exact inference over latent…
A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the general inverse…
The Mixed-Membership Stochastic Blockmodel~(MMSB) is proposed as one of the state-of-the-art Bayesian relational methods suitable for learning the complex hidden structure underlying the network data. However, the current formulation of…
In many, if not most, machine learning applications the training data is naturally heterogeneous (e.g. federated learning, adversarial attacks and domain adaptation in neural net training). Data heterogeneity is identified as one of the…
We provide new algorithms for two tasks relating to heterogeneous tabular datasets: clustering, and synthetic data generation. Tabular datasets typically consist of heterogeneous data types (numerical, ordinal, categorical) in columns, but…
Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by…
We begin the exploration of holographic duals to theories with generalised global (higher-form) symmetries. In particular, we focus on the case of magnetohydrodynamics (MHD) in strongly coupled plasmas by constructing and analysing a…
The review considers statistical systems composed of several phases that are intermixed in space at mesoscopic scale and systems representing a mixture of several components of microscopic objects. These types of mixtures should be…
There is a rich literature on clustering functional data with applications to time-series modeling, trajectory data, and even spatio-temporal applications. However, existing methods routinely perform global clustering that enforces…
We investigate a novel non-parametric regression-based clustering algorithm for longitudinal data analysis. Combining natural cubic splines with Gaussian mixture models (GMM), the algorithm can produce smooth cluster means that describe the…
We extend the stochastic reconstruction theorem to a setting where the underlying family of distributions satisfies some natural conditions involving rectangular increments. This allows us to prove the well-posedness of a new class of mixed…
Statistical modelling in the presence of data organized in groups is a crucial task in Bayesian statistics. The present paper conceives a mixture model based on a novel family of Bayesian priors designed for multilevel data and obtained by…
In the first part of this article, we will prove an existence-uniqueness result for generalized solutions of a mixed problem for linear hyperbolic system in the Colombeau algebra. In the second part, we apply this result to a wave…
The Partially Collapsed Gibbs (PCG) sampler offers a new strategy for improving the convergence of a Gibbs sampler. PCG achieves faster convergence by reducing the conditioning in some of the draws of its parent Gibbs sampler. Although this…
In this paper, we introduce a mixture of skew-t factor analyzers as well as a family of mixture models based thereon. The mixture of skew-t distributions model that we use arises as a limiting case of the mixture of generalized hyperbolic…
In this work we introduce a mixture of GPs to address the data association problem, i.e. to label a group of observations according to the sources that generated them. Unlike several previously proposed GP mixtures, the novel mixture has…
We present a geometric version of Quickest Change Detection (QCD) and Quickest Hub Discovery (QHD) tests in correlation structures that allows us to include and combine new information with distance metrics. The topic falls within the scope…
Machine learning has made tremendous progress in recent years, with models matching or even surpassing humans on a series of specialized tasks. One key element behind the progress of machine learning in recent years has been the ability to…